Cyclic edge-cuts in fullerene graphs

In this paper, we study cyclic edge-cuts in fullerene graphs. First, we show that the cyclic edge-cuts of a fullerene graph can be constructed from its trivial cyclic 5- and 6-edge-cuts using three basic operations. This result immediatelly implies the fact that fullerene graphs are cyclically 5-edge-connected. Next, we characterize a class of nanotubes as the only fullerene graphs with non-trivial cyclic 5-edge-cuts. A similar result is also given for cyclic 6-edge-cuts of fullerene graphs.     

New isomerization operations for fullerene graphs

The problem of topological isomerization operations for fullerenes is considered. Two basic classes of isomerization transformations admissible for fullerene graphs are proposed: rotation and mirror reflection of a chosen part of fullerene graph. Pyracylene and generalized Stone-Wales rearrangements are only the specific cases of extended isomerization operations for the fullerene graphs.     

Fullerene graphs have exponentially many perfect matchings

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.     

Saturation number of fullerene graphs

Saturation number of a graph G is the minimum possible size of a maximal matching in G. We establish improved upper and lower bounds on the saturation number in fullerene graphs and discuss their sharpness and quality.     

A note on the cyclical edge-connectivity of fullerene graphs

A fullerene graph is a 3-regular (cubic) and 3-connected spherical graph that has exactly 12 pentagonal faces and other hexagonal faces. The cyclical edge-connectivity of a graph G is the maximum integer k such that G cannot be separated into two components, each containing a cycle, by deletion of fewer than k edges. Došlić proved that the cyclical edge-connectivity of every fullerene graph is equal to 5. By using Euler’s formula, we give a simplified proof, mending a small oversight in Došlić’s proof. Further, it is proved that the cyclical connectivity of every fullerene graph is also equal to 5.     

Heck reaction on fullerene derivatives

The Heck reaction on fullerene-based aryl iodides has been achieved for the first time in good yields by using microwave irradiation.     

Cyclic 7-edge-cuts in fullerene graphs

A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerate and non-degenerate cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-degenerate cyclic 7-edge-cut in a fullerene graph, then the graph is a nanotube unless it is one of the two exceptions presented. We determined that there are 57 configurations of degenerate cyclic 7-edge-cuts, and we listed all of them.     

Synthesis of novel fullerene amino acids and their multifullerene peptides

[60]-Fullerene functionalized amino acids with 4-6 methylene spacers from α-carbon to the nitrogen atom of fulleropyrolidine and corresponding multifullerene peptides have been synthesized.     

Carbon nanotubes and fullerene in the solution polymerisation of acrylonitrile

The radical activity of single wall carbon nanotubes (SWCNT) and fullerene C₆₀ in the radical polymerisation of acrylonitrile (AN) in N,N-dimethylformamide (DMF) initiated by 2,2′-azobis[2-methyl-ω-hydroxy-oligo(oxyethylene) propionate] [AIB-OOE(4 0 0)] and 2,2′-azoisobutyronitrile (AIBN) at 333 K was investigated in situ using a dilatometric method. The carbonaceous substances were sonicated in DMF before the polymerisation. The changes in the process proceeding in the presence of SWCNT and C₆₀ in a comparison to the course of AN polymerisation without the participation of carbonaceous substances (the decrease of the reaction rate, the induction time) indicated on the inhibition effect, which can be described quantitatively using the inhibition parameter F. Single wall carbon nanotubes were found to act as retarders whereas fullerene C₆₀ as an inhibitor in the AN polymerisation. The changes in the chemical structure of products reveal that the carbon nanotubes and fullerenes are chemically bonded with the polymer.     

CoSALEN as a new catalyst for oxidation of fullerene C60

The effect of CoSALEN on anti-oxidative properties of fullerene C₆₀ in the presence of O₂ in cumene was investigated. A comparison was made between the role of the CoSALEN as a catalyst in the C₆₀ oxidation and oxidation in the presence of an initiator, i.e., AIBN. A mechanism is proposed for the catalytic role of CoSALEN in oxidation of C₆₀. Oxidation of octadecylaminofullerene C₆₀ at the same conditions reveals that oxidation could be a result of hydroperoxidation of the unreacted sites of C₆₀. We conclude that C₆₀ as well as its amino-derivatives enhance the efficiency of CoSALEN in the oxidation of cumene due to their radical scavenging property of their unreacted double-bond sites.     

Complex formation between water-soluble sulfonated calixarenes and C60 fullerene

The inclusion complexes of sulfonated thiacalix[4]arene 1 and calix[6]arene 2 sodium salts with C₆₀ fullerene were investigated by photoluminescence (PL) and quantum-chemical methods. The stoichiometries of calixarene/C₆₀ complexes were found to be 2:1 for 1 and 1:1 for 2. Related quantum-chemical investigations show that C₆₀ fullerene is included in a cavity composed of two half-bowl molecules of 1. The C₆₀ fullerene ball is located deep within the cavity of 2 and the negatively charged sulfonate arms probably inhibit the formation of the bowl-shaped capsule that was observed in the case of 1.     

A novel phthalocyanine with two axial fullerene substituents

A silicon phthalocyanine with two axial fullerene substituents was synthesized, and its electrochemical, absorption- and film-properties were characterized.     

Longest cycles in generalized Buckminsterfullerene graphs

It is shown that every regular 3-valent polyhedral graph whose faces are all 5-gons and 6-gons contains a cycle through at least 4/5 of its vertices.     

Novel addition in trifluoromethylation of [70]fullerene

Pyrolytic trifluoromethylation of [70]fullerene with CF₃CO₂Ag at 300 °C results in the addition of up to 12 CF₃ groups to the fullerene cage. Forty-six C₇₀(CF₃)_n derivatives (numbers in parentheses) were separated by two-stage high pressure liquid chromatography (HPLC) as follows: n = 2(2), 4(16), 6(9), 8(14) 10(5), some being characterised by NMR. The range of derivatives is much greater than for other [70]fullerene reactions, and as with [60]fullerene trifluoromethylation, no single derivative is dominant, indicating that kinetic stability mainly controls product formation. NMR spectra show most derivatives to be unsymmetrical, with combinations of quartets and septets (overlapping quartets) due to contiguous (‘linear’) addend arrays, having significantly different coupling constants of the ‘terminal’ quartets of between 9.1 and 17.7 Hz. These differences, together with those observed previously in trifluoromethylation of [60]fullerene are consistent with addition across both 6:6- and 5:6-ring junctions. Of the two C₇₀(CF₃)₂ isomers, one has either C_s or C₂ symmetry, the other has C₁ symmetry, whilst the C₇₀(CF₃)₄ derivatives fall into four categories: (i) symmetrical compounds (one gives only two singlets in the NMR); (ii) unsymmetrical compounds that show a ‘linear’ coupling sequence; (iii) unsymmetrical compounds having a remote pairs of adjacent groups; (iv) compounds having a coupled array of three CF₃ groups, together with a remote group suggesting sterically-driven migration. The first evaluation of differential NMR couplings across 6:6- and 5:6-bonds in a fullerene has been made using C₆₀F₆ as a model.     

Co-aggregation of fullerene C60 and thiophene in the non-aromatic solvent cyclohexene

Co-aggregation of fullerene C₆₀ and thiophene has been studied calorimetrically in cyclohexene at 25 °C. The total aggregation heat is found to depend on initial concentration of thiophene and fall between −1.9 and −5.8 kJ mol⁻¹. The corresponding thiophene/fullerene molar ratio (“co-aggregation number”) ranges from 7 to 12. The data are rationalized by formation of heteromolecular nanoaggregates with intermolecular contacts of both fullerene–thiophene and fullerene–fullerene types. A physical model describing interaction between fullerenes and π-donors in solution is substantiated and used to explain heterogeneity of composites containing fullerenes.     

Multiple hydrogen-bond-induced supramolecular nanostructure from a pincer-like molecule and a [60]fullerene derivative

A new supramolecular self-assembled system between a perylene bisimide bearing diaminopyridine-substituted isophthalamide groups (PP) and a [60]fullerene containing barbituric acid moiety (C₆₀bar) through a complementary six-point hydrogen-bonding interaction was constructed. The formation of hydrogen bonding was confirmed by ¹H NMR spectra studies in CDCl₃. Fluorescence quenching experiments indicated that the fluorescence of PP was greatly quenched by the hydrogen-bonded C₆₀bar (K_sv=2.71×10⁴ M⁻¹). A steady and rapid cathodic 0.15 μA cm⁻² photocurrent response of the PP/C₆₀bar film deposited onto an ITO electrode was produced under the irradiation of 20 mW cm⁻² white light, indicating the presence of photo-induced electron transfer between PP and C₆₀bar. TEM images showed that spherical particles were fabricated by the self-assembly of PP and C₆₀bar through hydrogen-bonding interaction.     

Directed graphs of structurally stable potential energy surfaces representing a-priori reaction pathways

An intrinsic property of potential energy surfaces (PES) that holds within the adiabatic approximation is established: its structural stability.We derive the condition that ensures this property: There cannot be any integral curve of the gradient field of the PES that connects two classical transition state configurations without passing through another critical configuration in between.Under this situation, we can establish a one-to-one correspondence: a whole class of adiabatic PES defining one reaction mechanism is associated to a directed graph. Thus, the problem of finding a-priori pathways involving a given number m of chemical species narrows down to a classifying certain directed graphs with m sinks. The combinatorial method is derived in this paper.Detailed examples on a-priori pathways for degenerate thermal rearrangements and on 1-2 hydrocarbon shifts are worked out and found in agreement with experimental evidence.     

Radical scavenging efficiency of different fullerenes C60-C70 and fullerene soot

This investigation was undertaken to determine the antioxidant activity of a range of fullerenes C₆₀ and C₇₀ in order to rank them according to their comparative efficiency. The model reaction of initiated (2,2′- azobisisobutyronitrile, AIBN) cumene oxidation was used to determine rate constants for addition of radicals to fullerenes. Measurements of oxidation rates in the presence of different fullerenes showed that the antioxidant activity as well as the mechanism and mode of inhibition were different for fullerenes C₆₀ and C₇₀ and fullerene soot. All fullerenes - C₆₀ of gold grade, C₆₀/C₇₀ (93/7, mix 1), C₆₀/C₇₀ (80 ± 5/20 ± 5, mix 2) and C₇₀ operated as alkyl radical acceptora, whereas fullerene soot surprisingly retarded the model reaction by a dual mode similar to that for the fullerenes and with an induction period like many of the sterically hindered phenolic and amine antioxidants. For the C₆₀ and C₇₀ the oxidation rates were found to depend linearly on the reciprocal square root of the concentration over a sufficiently wide range thereby fitting the mechanism for the addition of cumylalkyl radicals to the fullerene core. This is consistent with literature data on the more ready and rapid addition of alkyl and alkoxy radicals to the fullerenes compared with peroxy radicals. Rate constants for the addition of cumyl radicals to the fullerenes were determined to be k_(333K) = (1.9 ± 0.2) × 10⁸ (C₆₀); (2.3 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 1); (2.7 ± 0.2) × 10⁸ (C₆₀/C₇₀, mix 2); (3.0 ± 0.3) × 10⁸ (C₇₀), M⁻¹ s⁻¹. The increasing C₇₀ constituent in the fullerenes leads to a corresponding increase in the rate constant.The fullerene soot inhibits the model reaction according to the mechanism of trapping of peroxy radicals; the oxidation proceeds with a pronounced induction period and kinetic curves are linear in semi-logarithmic coordinates.For the first time the effective concentration of inhibiting centres and inhibition rate constants for the fullerene soot have been determined to be fn[C₆₀−soot] = (2.0 ± 0.1) × 10⁻⁴ mol g⁻¹ and k_inh = (6.5 ± 1.5) × 10³ M⁻¹ s⁻¹ respectively.The kinetic data obtained specify the level of antioxidant activity for the commercial fullerenes and scope for their rational use in different composites. The results may be helpful for designing an optimal profile of composites containing fullerenes.     

Perylene-3,4:9,10-bis(dicarboximide) linked to [60]fullerene as a light-harvesting antenna

New [60]fullerene-perylene-3,4:9,10-bis(dicarboximide) dyads 1 and 2 are described in the search of an energy transfer from the dye as a photoactive antenna to the fullerene moiety.